ref_stability.bib

@incollection{sontagStabilityFeedbackStabilization2009,
  title = {Stability and {{Feedback Stabilization}}},
  booktitle = {Encyclopedia of {{Complexity}} and {{Systems Science}}},
  author = {Sontag, Eduardo D.},
  editor = {Meyers, Robert A.},
  year = {2009},
  pages = {8616--8630},
  publisher = {Springer},
  address = {New York, NY},
  doi = {10.1007/978-0-387-30440-3_515},
  url = {https://doi.org/10.1007/978-0-387-30440-3_515},
  urldate = {2022-10-25},
  isbn = {978-0-387-30440-3},
  langid = {english}
}

@incollection{brockettAsymptoticStabilityFeedback1983,
  title = {Asymptotic Stability and Feedback Stabilization},
  booktitle = {Differential {{Geometric Control Theory}}},
  author = {Brockett, R.},
  editor = {Brockett, R. and Millman, R. and Sussmann, H.},
  year = {1983},
  publisher = {Birkh{\"a}user},
  address = {Boston}
}

@book{michelStabilityDynamicalSystems2015,
  title = {Stability of {{Dynamical Systems}}: {{On}} the {{Role}} of {{Monotonic}} and {{Non-Monotonic Lyapunov Functions}}},
  shorttitle = {Stability of {{Dynamical Systems}}},
  author = {Michel, Anthony N. and Hou, Ling and Liu, Derong},
  year = {10 dubna 2015},
  series = {Systems \& {{Control}}: {{Foundations}} \& {{Applications}}},
  edition = {2},
  publisher = {Birkh{\"a}user},
  address = {Cham},
  url = {https://doi.org/10.1007/978-3-319-15275-2},
  abstract = {The second edition of this textbook ~provides a single source for the analysis of system models represented by continuous-time and discrete-time, finite-dimensional and infinite-dimensional, and continuous and discontinuous dynamical systems.~ For these system models, it presents results which comprise the classical Lyapunov stability theory involving monotonic Lyapunov functions, as well as corresponding contemporary stability results involving non-monotonic Lyapunov functions.~ Specific examples from several diverse areas are given to demonstrate the applicability of the developed theory to many important classes of systems, including digital control systems, nonlinear regulator systems, pulse-width-modulated feedback control systems, and artificial neural networks.~The authors cover the following four general topics:~-~Representation and modeling of dynamical systems of the types described above-~Presentation of Lyapunov and Lagrange stability theory for dynamical systems defined on general metric spaces involving monotonic and non-monotonic Lyapunov functions-~Specialization of this stability theory to finite-dimensional dynamical systems -~Specialization of this stability theory to infinite-dimensional dynamical systemsReplete with examples and requiring only a basic knowledge of linear algebra, analysis, and differential equations, this book can be used as a textbook for graduate courses in stability theory of dynamical systems.~ It may also serve as a self-study reference for graduate students, researchers, and practitioners in applied mathematics, engineering, computer science, economics, and the physical and life sciences.Review of the First Edition:``The authors have done an excellent job maintaining the rigor of the presentation, and in providing standalone statements for diverse types of systems.~ [This] is a very interesting book which complements the existing literature. [It] is clearly written, and difficult concepts are illustrated by means of good examples.'' - Alessandro Astolfi, IEEE Control Systems Magazine, February 2009},
  isbn = {978-3-319-15274-5}
}

@article{lacerdaStabilityUncertainSystems2017,
  title = {Stability of Uncertain Systems Using {{Lyapunov}} Functions with Non-Monotonic Terms},
  author = {Lacerda, M{\'a}rcio J. and Seiler, Peter},
  year = {2017},
  month = aug,
  journal = {Automatica},
  volume = {82},
  pages = {187--193},
  issn = {0005-1098},
  doi = {10.1016/j.automatica.2017.04.042},
  url = {https://www.sciencedirect.com/science/article/pii/S0005109817302364},
  urldate = {2023-11-19},
  abstract = {This paper is concerned with the problem of robust stability of uncertain linear time-invariant systems in polytopic domains. The main contribution is to present a systematic procedure to check the stability of the uncertain systems by using an arbitrary number of quadratic functions within higher order derivatives of the vector field in the continuous-time case and higher order differences of the vector field in the discrete-time case. The matrices of the Lyapunov function appear decoupled from the dynamic matrix of the system in the conditions. This fact leads to sufficient conditions that are given in terms of Linear Matrix Inequalities defined at the vertices of the polytope. The proposed method does not impose sign condition constraints in the quadratic functions that compose the Lyapunov function individually. Moreover, some of the quadratic functions do not decrease monotonically along trajectories. However, if the sufficient conditions are satisfied, then a monotonic standard Lyapunov function that depends on the dynamics of the uncertain system can be constructed a posteriori. Numerical examples from the literature are provided to illustrate the proposed approach.}
}

@article{linsenmayerPeriodicEventtriggeredControl2019,
  title = {Periodic Event-Triggered Control for Networked Control Systems Based on Non-Monotonic {{Lyapunov}} Functions},
  author = {Linsenmayer, Steffen and Dimarogonas, Dimos V. and Allg{\"o}wer, Frank},
  year = {2019},
  month = aug,
  journal = {Automatica},
  volume = {106},
  pages = {35--46},
  issn = {0005-1098},
  doi = {10.1016/j.automatica.2019.04.039},
  url = {https://www.sciencedirect.com/science/article/pii/S0005109819301992},
  urldate = {2023-11-19},
  abstract = {This article considers exponential stabilization of linear Networked Control Systems with periodic event-triggered control for a given network specification in terms of a maximum number of successive dropouts and a constant transmission delay. Based on stability results using non-monotonic Lyapunov functions for discontinuous dynamical systems, two sufficient results for stability of the general model of a linear event-triggered Networked Control System are derived. Those results are used to derive robust periodic event-triggered control strategies. First, a static triggering mechanism for the case without delay is derived. Afterwards, two dynamic triggering mechanisms are developed for the case without and with delay. It is shown how a degree of freedom, being contained in the dynamic triggering mechanisms, can be used to shape the resulting network traffic. The applied adaption technique is motivated by existing congestion control mechanisms in communication networks. The properties of the derived mechanisms are illustrated in a numerical example.}
}

@article{yorkeTheoremLiapunovFunctions1970,
  title = {A {{Theorem}} on {{Liapunov Functions Using}} \${\textbackslash}ddot {{V}}\$},
  author = {Yorke, James A},
  year = {1970},
  month = mar,
  journal = {Mathematical Systems Theory},
  volume = {4},
  number = {1},
  pages = {40--45},
  url = {https://link.springer.com/article/10.1007/BF01705884},
  langid = {english}
}

@article{heinenLagrangeStabilityHigher1970,
  title = {Lagrange Stability and Higher Order Derivatives of {{Liapunov}} Functions},
  author = {Heinen, J.A. and Vidyasagar, M.},
  year = {1970},
  month = jul,
  journal = {Proceedings of the IEEE},
  volume = {58},
  number = {7},
  pages = {1174--1174},
  issn = {1558-2256},
  doi = {10.1109/PROC.1970.7890},
  url = {https://ieeexplore.ieee.org/abstract/document/1449820},
  urldate = {2023-11-20},
  abstract = {It is shown that the Lagrange stability of an autonomous system can be determined on the basis of the existence of a Liapunov function and the satisfaction of a certain inequality involving its first three derivatives.}
}